In this paper, two different methods, Legendre orthogonal polynomial method (LOPM) and Global matrix method (GMM), are combined with the couple-stress theory to investigate the reflection and transmission of P wave in a functionally graded (FG) couple-stressed plate immersed in liquid. The GMM needs to divide the FG plate into the multilayered model, with each layer containing six partial waves. However, the LOPM only expands the displacement vectors in the FG couple-stressed plate into the Legendre orthogonal polynomial series. The paper shows that both methods are in good agreement. Nevertheless, the proposed LOPM is more efficient for the FG microstructure because it does not require plate delamination and calculation of the displacements of each partial wave. It also shows that the couple-stress effect affects the resonant frequencies of the FG plate, decreasing the number of resonant frequencies. By controlling the gradient field, some resonances can be avoided.

中文翻译：

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基于修正偶应力理论的弹性波通过功能梯度微结构板传播的理论研究

在本文中，勒让德正交多项式法（LOPM）和全局矩阵法（GMM）两种不同的方法结合耦合应力理论，研究了功能梯度（FG）耦合应力中 P 波的反射和传输。盘浸入液体中。GMM 需要将 FG 板划分为多层模型，每层包含 6 个分波。然而，LOPM 仅将 FG 耦合应力板中的位移矢量扩展为 Legendre 正交多项式级数。论文表明，这两种方法具有很好的一致性。然而，所提出的 LOPM 对于 FG 微结构更有效，因为它不需要板分层和计算每个分波的位移。它还表明耦合应力效应影响 FG 板的共振频率，减少共振频率的数量。通过控制梯度场，可以避免一些共振。